DIFFERENtIAl & DIFFERENCE EqUAtIONS ANd APPlICAtIONS

ANNULAR JET AND COAXIAL JET FLOW
JOSHUA DU AND JUN JI
The dispersion relations for supersonic, in-viscid, and compressible jet flow of annular
and coaxial jets under vortex sheet model are derived. The dispersion relation in either
case, in a form of determinant of a 4 × 4 matrix, is an implicit function of ω and wave
number κ, and provides the foundation to investigate Kelvin-Helmholtz instability and
acoustic waves. The dispersion relation of jet flow under more realistic model, like finite
thickness model, can also be derived.
Copyright © 2006 J. Du and J. Ji. This is an open access article distributed under the Creative
Commons Attribution License, which permits unrestricted use, distribution, and
reproduction in any medium, provided the original work is properly cited.
1. Introduction
Jet aircrafts were introduced right after the Second World War. Because of the very high
speed of the jet, and the large tangential gradient of the velocity of jet flow, the Kelvin-
Helmholtz instability waves caused the instability and dramatically reduced life spans of
jets. Hence jet noise prediction and reduction became important economical, environmental,
and safety issues.
Many researchers, like Tam and Morris [6], Tam and Burton [3, 4], and Tam and
Hu [5], found that Kelvin-Helmholtz instability waves in supersonic jets constitute the
basic elements of the feedback loop responsible for the generation of multiple-jet resonance
tones. They successfully modeled the jet flow and interpreted the characteristics of
instability waves and upstream propagated acoustic wave through numerical computation.
Atthesametimemanyresearchers,likeMorrisetal.[1], Wlezien [9], Tam and Ahuja
[2], Tam and Norum [7], and Tam and Thies [8], also investigated the problems of how
jet nozzles of different geometries affect the generation of the instability wave, focusing
on rectangular jets.
We are interested in studying annular and coaxial jets. In this paper, we modeled the
jet flow and derived dispersion relations for single annular and coaxial jet flow as an
introduction to the investigation of multiple annular and coaxial jets flow.
Hindawi Publishing Corporation
Proceedings of the Conference on Differential & Difference Equations and Applications, pp. 383–390